If cosA=cos B, then when does A=B? (Always, sometimes, never, infinite etc).
it is always the same when it is a sign identity
$\displaystyle \cos\left({\theta}\right) = \cos\left({-\theta}\right)$
since $\displaystyle \beta$ would just be a reflection of $\displaystyle \alpha$ off the x axis then
$\displaystyle \cos{\alpha} = \cos{\beta}$
example:
$\displaystyle \cos\left({\frac{\pi}{4}}\right)
=\cos\left({-\frac{\pi}{4}}\right)
= \frac{\sqrt{2}}{2}$